New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2015 · Shift 0 · Q26

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2015 · Shift 0 · Q26

Quadratic Equation and Inequalities question

2015 · Shift 0 · Q26

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\alpha

and

\beta

be the roots of equation

{x^2} - 6x - 2 = 0

. If

{a_n} = {\alpha ^n} - {\beta ^n},

for

n \ge 1,

then the value of

{{{a_{10}} - 2{a_8}} \over {2{a_9}}}

is equal to :

A
$3$
B
$- 3$
C
$6$
D
$- 6$

More from Quadratic Equation and Inequalities

Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p e 0.$ If $p, q, r$ in A.P. and $\frac{1}{α} + \frac{1}{β} = 4,$ then the value of $∣ α - β ∣$ is :2014 · MCQ
If $a \in R$ and the equation $- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0$ (where [ $x$ ] denotes the greater integer $\leq x$ ) has no integral solution, then all possible values of a…2014 · MCQ
If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is2013 · MCQ
The equation $e^{s i n x} - e^{- s i n x} - 4 = 0$ has:2012 · MCQ
If $α$ and $β$ are the roots of the equation $x^{2} - x + 1 = 0,$ then $α^{2009} + β^{2009} =$ 2010 · MCQ
If the roots of the equation $b x^{2} + c x + a = 0$ imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is :2009 · MCQ
The quadratic equations $x^{2} - 6 x + a = 0$ and $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is2008 · MCQ
STATEMENT - 1 : For every natural number $n \geq 2, \frac{1}{1} + \frac{1}{2} + ........ + \frac{1}{n} > n .$ STATEMENT - 2 : For every natural number $n \geq 2,$ , $n (n + 1) < n + 1.$ 2008 · MCQ